Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

State whether the given sentence is true or false. If false, replace the underlined term to make a true sentence.

The graph of a quadratic function has a maximum if the coefficient of the x2is positive.

Short Answer

Expert verified

The sentence, “The graph of a quadratic function has a maximum if the coefficient of the x2 is positive” is false.

The correct replacement for the underlined term to make a true sentence is minimum.

Step by step solution

01

Step 1. Define the standard form of the quadratic function.

A quadratic function, which is written in the form, y=ax2+bx+c, where, a0is called the standard form of the quadratic function.

02

Step 2. Define the maximum point of a function.

The maximum value of a function is the place where the function reaches its highest point.

03

Step 3. Check whether the given sentence is true or false.

The graph of the parabola y=ax2+bx+c,

Opens upward and has a minimum value at x=b2a, when a>0.

Opens downward and has a maximum value at x=b2a, when a<0.

Therefore, the sentence, “The graph of a quadratic function has a maximum if the coefficient of thex2 is positive” is false.

The correct replacement for the underlined term to make a true sentence is minimum.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Study anywhere. Anytime. Across all devices.

Sign-up for free